Van Persie suffered ankle ligament damage during the Netherlands' friendly against Italy on November 14 and is expected to be out until April.
"We are working on this with our lawyers and we are definitely going for it," Wenger was quoted as saying on the BBC on Sunday. "I expect compensation for the damage it can make to the championship."
Wenger believes the Dutch authorities initially misdiagnosed Van Persie's injury and that he wasted crucial time travelling to Serbia to see a doctor who has treated several players using fluids derived from horse placenta.
"Initially, the Dutch FA said it was a small problem and Robin called me to see if he could go and see this Serbian wonder doctor and it was okay," Wenger said.
"It was only when he came back here that we realised there was much more damage. In Holland they have a fight between the national doctor and the guy that did the surgery on Robin."
The Dutch Federation (KNVB) issued a statement last month denying any wrongdoing over the diagnosis of Van Persie's injury.
"The medical staff of the KNVB contacted Arsenal club doctor Gary O'Driscoll the same Sunday to inform him about the outcome of the investigation and to transfer the medical record regarding this injury," their statement said. "The scan was also handed over to the medical staff of Arsenal."
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